Baba does claim to have wrestled a bear in The Kite Runner by Khaled Hosseini. In chapter three, Amir talks about his father and the bear.
Lore has it my father once wrestled a black bear in Baluchistan with his bare hands. If the story had been about anyone else, it would have been dismissed as laaf, that Afghan tendency to exaggerate.... But no one ever doubted the veracity of any story about Baba. And if they did, well, Baba did have those three parallel scars coursing a jagged path down his back.
It is interesting to note that Amir does not say that his father told him the story; he says "lore has it," which implies that Amir has heard the story told by others rather than directly from his father. Despite the Afghan tendency to make things sound much grander than they are, there is corroborating evidence here: the scar which could have come from a bear paw running across Baba's back.
If the story is true, wrestling a bear could certainly be seen as courage. It could also be considered foolhardy and rash, however, since he could have gotten himself killed. Since bear-wrestling is a sport, it is not quite as courageous as meeting and defeating a bear in the wild, but it certainly requires bravery to go one-on-one with a bear. It is accurate to say that Baba did display courage when he wrestled the bear.